Ordinary Differential Equations II (MAE716)

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General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	MAE716
Semester	7
Course Title	Differential Equations I
Independent Teaching Activities	Lectures (Weekly Teaching Hours: 3, Credits: 6)
Course Type	Special Background
Prerequisite Courses	-
Language of Instruction and Examinations	Language of Instruction (lectures): Greek Language of Instruction (activities other than lectures): Greek and English Language of Examinations: Greek and English
Is the Course Offered to Erasmus Students	Yes
Course Website (URL)	See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

Bloom's Taxonomy. (1) Remembering: The notion of fixed point, of maximum domain of solutions and of the stability of not necessarily linear ODE's. (2) Comprehension: Study fixed point theorems and Topological Degree Theory, with applications to not necessarily linear ODE's. Study the maximum domain of solutions of not necessarily linear ODE's. Linearization of ODE's. (3) Applying: Study related real world problems. (4) Evaluating: Teaching secondary school courses.

General Competences

Working independently and in groups. Production of free, creative and inductive thinking. Creative, analytic and synthetic thinking.

Syllabus

Ενότητα 1. Συναρτησιακές Διαφορικές Εξισώσεις: Λόγοι ύπαρξης τέτοιων εξισώσεων, Ύπαρξη και μονοσήμαντο λύσεων, Εύρεση λύσεων, Ευστάθεια, Γραμμικά και μη γραμμικά συστήματα. Ενότητα 2. Ολοκληρωτικές Εξισώσεις: Λόγοι ύπαρξης τέτοιων εξισώσεων, Εξισώσεις Fredholm, Εξισώσεις Volterra, Ολοκληρωτικό-Διαφορικές Εξισώσεις, Πρόβλημα Abel, Μη γραμμικές ολοκληρωτικές εξισώσεις. Ενότητα 3. Εξισώσεις Διαφορών: Λόγοι ύπαρξης τέτοιων εξισώσεων, Εύρεση αναλυτικού τύπου για γραμμικές ΕΔ, Γραμμικοποίηση μη γραμμικών ΕΔ, Συστήματα ΕΔ, Ευστάθεια με έμφαση στη μέθοδο Lyapunov.

Teaching and Learning Methods - Evaluation

Delivery	Lectures in class. Teaching is assisted by Learning Management System. Teaching is assisted by the use of online forums where students can participate in order to improve their problem solving skills, as well as their understanding of the theory they are taught. Teaching is assisted by the use of pre-recorded videos.
Use of Information and Communications Technology	Use of Learning Management System, combined with File Sharing Platform as well as Blog Management System for distributing teaching material, submission of assignments, course announcements, gradebook keeping for all students evaluation procedures, communicating with students. Use of Appointment Scheduling System for organising appointments between students and the teacher. Use of Survey Web Application for submitting anonymous evaluations regarding the teacher. Use of Wiki Engine for publishing manuals regarding the regulations applied at the exams processes, the way teaching is organized, the grading methods, as well as the use of the online tools used within the course.
Teaching Methods	Activity Semester Workload Lectures (7x3) 21 Seminars (6x3) 18 Individual study 78 Exrecises/projects 33 Course total 150
Student Performance Evaluation	Language of evaluation: Greek and English. Methods of evaluation: Weekly written assignments. Few number of tests during the semester. Based on their grades in the aforementioned weekly assignments and tests, limited number of students can participate in exams towards the end of the semester, before the beginning of the exams period. In any case, all students can participate in written exams at the end of the semester, during the exams period. The aforementioned information along with all the required details are available through the course's website. The information is explained in detail at the beginning of the semester, as well as, throughout the semester, during the lectures. Reminders are also posted at the beginning of the semester and throughout the semester, through the course's website. Upon request, all the information is provided using email or social networks.

Attached Bibliography

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

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